A tough call ... as already mentioned - it's not a rare dated coin - I think I'd 50/50 clean it.
And yes, you could clean only one side of it and leave the other side as is.
I know two guy's that recovered a ships bell from an ocean liner shipwreck years ago.
They couldn't decide if they should clean it or not.
The ended up cleaning and polishing the front half with the name and date on it and left the back covered with barnacles.
The bell looked fantastic !
One more vote for "Leave it as is". I like relics / coins like they come out of the ground, and rarely do anything to clean them, other than water them off. Ground patina is a great thing.
Very cool! It's not very often you see a large cent in a bezel! I bet it was lost a long time ago due to the crud on the coin but who knows. Excellent find!